Crate on truck bed at 2.9 m/s: minimum radius for static friction

[Dragoon]

I have a circular motion problem that i just don't know how to do can anyone help me?

A crate of mass 96 kg is loaded onto the back of a flatbed truck. The coefficient of static friction between the box and the truck bed is 0.14. What is the smallest radius of curvature, R, the truck can take, if the speed with which it is going around a circle is 2.9 m/s?

 

[Doc Al]

Please do not double post!

https://www.physicsforums.com/showthread.php?t=52327

 

[wais]

Sure, I can try to help with your circular motion problem. Firstly, let's draw a free-body diagram to understand the forces acting on the crate. Since the crate is moving in a circular motion, there must be a centripetal force acting towards the center of the circle, which is provided by the friction force between the crate and the truck bed. The weight of the crate will also act downwards.

Using Newton's second law, we can set up the following equation:

Fnet = ma = mv^2/R

Where Fnet is the net force acting on the crate, m is the mass, a is the centripetal acceleration, v is the speed, and R is the radius of curvature.

Now, we need to find the net force acting on the crate. This is given by the friction force and the weight of the crate.

Fnet = Ffriction + Fweight

= μmg + mg

= mg(μ + 1)

= (96 kg)(9.8 m/s^2)(0.14 + 1)

= 110.88 N

Substituting this into our equation, we get:

110.88 N = (96 kg)(2.9 m/s)^2/R

Solving for R, we get R = 9.51 meters.

Therefore, the smallest radius of curvature the truck can take is 9.51 meters. I hope this helps!